Rough Set Processing of Vague Information Using Fuzzy Similarity Relations

2000 ◽  
pp. 149-173 ◽  
Author(s):  
Salvatore Greco ◽  
Benedetto Matarazzo ◽  
Roman Slowinski
Keyword(s):  
Rough Set ◽  
Similarity Relations ◽  
Fuzzy Similarity

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Comparison of Dispersion Models by Using Fuzzy Similarity Relations

2011 ◽  
pp. 57-67 ◽  
Author(s):  
Angelo Ciaramella ◽  
Angelo Riccio ◽  
Stefano Galmarini ◽  
Giulio Giunta ◽  
Slawomir Potempski
Keyword(s):  
Dispersion Models ◽  
Similarity Relations ◽  
Fuzzy Similarity

Fuzzy Similarity Relations in Decision Making

2020 ◽  
pp. 369-385 ◽  
Author(s):  
Mohamed El Alaoui ◽  
Khalid El Yassini
Keyword(s):  
Decision Making ◽  
Human Knowledge ◽  
Similarity Relations ◽  
Fuzzy Similarity ◽  
Context Of Use

Similarity is an ambiguous term that can be interpreted differently depending on the context of use. In this chapter, the authors review some of its uses before focusing on decision making. Ignoring the uncertainty of human knowledge would be denying a major attribute. Thus, they linked it to the fuzzy context. However, even taking this aspect into consideration, the opinion itself must be relevant. Therefore, the more a decision is similar to other opinions, the more it is coherent. Hence, there is a need to measure the similarity between each couple of expressed opinions.

A fuzzy similarity-based rough set approach for attribute selection in set-valued information systems

2019 ◽  
Vol 24 (6) ◽  
pp. 4675-4691 ◽  
Author(s):  
Shivani Singh ◽  
Shivam Shreevastava ◽  
Tanmoy Som ◽  
Gaurav Somani
Keyword(s):  
Information Systems ◽  
Rough Set ◽  
Attribute Selection ◽  
Fuzzy Similarity

Variable Precision Rough Set Model in Information Tables with Missing Values

2011 ◽  
Vol 15 (1) ◽  
pp. 110-116 ◽  
Author(s):  
Yoshifumi Kusunoki ◽  
◽  
Masahiro Inuiguchi
Keyword(s):  
Rough Set ◽  
Missing Values ◽  
Complete Information ◽  
Misclassification Error ◽  
Lower And Upper Bounds ◽  
Variable Precision ◽  
Similarity Relations ◽  
Proposed Model ◽  
Variable Precision Rough Set ◽  
Information Tables

In this paper, we study rough set models in information tables with missing values. The variable precision rough set model proposed by Ziarko tolerates misclassification error using a membership function in complete information tables. We generalize the variable precision rough set in information tables with missing values. Because of incompleteness, the membership degree of each objects becomes an interval value. We define six different approximate regions using the lower and upper bounds of membership functions. The properties of the proposed rough set model are investigated. Moreover we show that the proposed model is a generalization of rough set models based on similarity relations.

Fuzzy Attribute Reduction Based on Fuzzy Similarity

2014 ◽  
Vol 533 ◽  
pp. 237-241
Author(s):  
Xiao Jing Liu ◽  
Wei Feng Du ◽  
Xiao Min
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Decision Table ◽  
Reduction Algorithm ◽  
Fuzzy Decision ◽  
Core Content ◽  
Fuzzy Similarity

The measure of the significance of the attribute and attribute reduction is one of the core content of rough set theory. The classical rough set model based on equivalence relation, suitable for dealing with discrete-valued attributes. Fuzzy-rough set theory, integrating fuzzy set and rough set theory together, extending equivalence relation to fuzzy relation, can deal with fuzzy-valued attributes. By analyzing three problems of FRAR which is a fuzzy decision table attribute reduction algorithm having extensive use, this paper proposes a new reduction algorithm which has better overcome the problem, can handle larger fuzzy decision table. Experimental results show that our reduction algorithm is much quicker than the FRAR algorithm.

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